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Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor
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Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor H. Ghahraloud, M. Farsi∗ Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 31 August 2016 Revised 2 October 2017 Accepted 4 October 2017 Available online xxx Keywords: Methanol oxidation Process modeling Multi-objective optimization Pareto front TOPSIS decision making
a b s t r a c t The main objective of this study is modeling and optimization of methanol oxidation over ironmolybdenum oxide catalyst in a fixed bed reactor. The considered process is modeled based on the mass and energy balance equations at steady state condition. To verify accuracy of the proposed model and considered assumptions, the simulation results are compared with the plant data. Then, the effect of feed temperature, coolant temperature and air-to-methanol molar ratio on the reactor performance is investigated. In addition, considering formaldehyde production capacity and selectivity as objectives, a multi-objective optimization problem is formulated considering feed and coolant temperature, and air to methanol ratio as decision variables. Based on the developed mathematical model of the process and multi-objective optimization model, Pareto optimal front is obtained by non-sorting multi-objective genetic algorithm. Then, the single optimal point is selected from developed optimal Pareto front by TOPSIS decision-making method. The performance of the optimized reactor is compared with the conventional reactor at steady state condition. © 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Formaldehyde as the simplest aldehyde is an important compound to produce complex chemicals and polymers such as urea formaldehyde resin, melamine resin, phenol formaldehyde resin and polyoxymethylene plastics [1]. Formaldehyde is produced industrially from methanol through different processes, including partial oxidation and dehydrogenation in the presence of silver crystal or silver gauze with excess methanol, and oxidation only with air in the presence of a modified iron–molybdenum– vanadium oxide catalyst and excess air [2]. The main differences between the production methods are catalyst type, operating condition and the feed concentration. The methanol oxidation over silver-based catalyst at 60 0–70 0 °C is the oldest process to produce formaldehyde commercialized by BASF and ICI [1,3,4]. In this process, reaction temperature and conversion depend on the methanol concentration in feed stream. In Formox process, commercialized by Johnson Matthey Process Technologies, methanol and oxygen react at 30 0–40 0 °C in presence of iron–molybdenum oxide catalyst [1]. Generally, the iron– molybdenum oxide catalyst has attracted more attention compared to the silver catalyst due to lower investment and operating costs.
∗
Corresponding author. E-mail address: [email protected] (M. Farsi).
However, sensitivity against operating condition is the main disadvantage of iron–molybdenum oxide catalyst [3]. Many researchers have focused on the catalyst synthesis and mechanism of methanol oxidation to formaldehyde [5–14]. Andersson et al. presented a good overview describing the historical and present developments on the methanol oxidation to formaldehyde from 1950s [15]. Generally, vanadium pentoxide catalyst is the first metal oxide used in the methanol oxidation process [1]. Adkins and Peterson introduced iron–molybdenum oxide as methanol oxidation catalyst due to high selectivity and thermal resistance [16]. Galvanin et al. proposed a model-based design of experiments procedure to estimate the kinetic parameters of methanol oxidation on silver catalyst [17]. Chapman et al. showed that the performance of Mo-enriched, bulk ferric molybdate, employed commercially for selective oxidation of methanol to formaldehyde, is limited by a low surface area [18]. The results proved that core–shell, multi-component oxides offer new routes for improving catalytic performance and activity. Windes et al. modeled partial oxidation of methanol considering heterogeneous and pseudo homogeneous models at steady state condition. The results showed that the considered models are capable to predict hot spot position and yield. In addition, it was shown that coolant temperature has a significant effect on the reactor performance compared to the feed temperature [19]. Faliks et al. modeled formaldehyde production over iron–molybdenum oxide catalyst at steady state condition. The results showed that the distribution of heat flux effects
https://doi.org/10.1016/j.jtice.2017.10.003 1876-1070/© 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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Nomenclature av Ac Cp C D dp Ei Dij Dim F hf hi ho
H i ki Ka L P Pi ri R Tg Tc Ts ug U g yi ysi z
specific surface area of catalyst pellet (m2 /m3 ) cross section area of each tube (m2 ) specific heat of the gas at constant pressure (J/mol/K) total concentration (kmol/m3 ) tube diameter (m) catalyst particle diameter (m) activation energy for ith reaction (J/mol) binary diffusion coefficient of component i in j (m2 /s) diffusion coefficient of component i in the mixture (m2 /s) total molar flow rate (mol/s) gas–solid heat transfer coefficient in reactor (W/m2 /K) tube side heat transfer coefficient in reactor (W/m2 /K) shell side heat transfer coefficient in reactor (W/m2 /K) heat of reaction for reaction i (kJ/kmol) reaction rate constant (mol g/cat/h/kPa0.5 ) adsorption equilibrium constant in the rate equation (kPa−0.5 ) reactor length (m) total pressure (kPa) partial pressure of component i (kPa) rate of reaction (mol g/cat/h) Universal gas constant (J/mol/K) bulk gas phase temperature (K) cooling liquid temperature in shell side (K) solid phase temperature (K) velocity of fluid phase (m/s) overall heat transfer coefficient (W/m2 /K) mole fraction of component i in the fluid phase mole fraction of component i on the catalyst surface axial reactor coordinate (m)
Greek letters μ viscosity of gas phase (Pa s) η catalyst effectiveness factor ρ gas density (kg/m3 ) ρ catalytic bed density (kg/m3 ) b ε porosity factor
on the formaldehyde yield [20]. Yang et al. modeled a packed-bed membrane reactor for partial oxidation of methanol to formaldehyde. The simulation results showed that the membrane reactor presents a higher selectivity compared to the conventional process [21]. Moustafa simulated a formaldehyde reactor considering diffusion-reaction kinetic model [22]. The effectiveness factor of reactions was selected as fitting parameters and calculated based on the plant data. Process optimization is the discipline to adjust process condition to operate at desired performance without violating operational, safety and other constraints. Operating the chemical processes at optimal point could decrease cost, energy and risk in the system. There are many researches in the literature that have focused on the optimization of chemical process particularly chemical reactors [23]. Elnashaie et al. developed a heterogeneous model to simulate and optimize an industrial ammonia reactor [24]. The results showed that applying the optimal condition on the system increases ammonia production capacity about 6–7%. Kordabadi and
Table 1 Reactor characteristics and catalyst specification of the conventional process. Parameter
Value
Feed condition Coolant temperature (K) Methanol feed flow rate (kmol/h) Air to methanol ratio Inlet pressure (bar) Inlet temperature (K)
540 102.96 8.325 2.16 467
Reactor characteristics Catalyst bed length (m) Tube internal diameter (m) Number of tubes Bed void fraction
0.77 0.025 7700 0.45
Catalyst particle characteristics Catalyst shape Density (kg/m3 ) Diameter (m) Height to diameter ratio
Ring 10 0 0 0.0048 1
Jahanmiri optimized methanol production in an industrial fixed bed reactor by genetic algorithm [25]. This optimization approach enhanced 2.9% additional yield throughout 4 years. Farsi and Shahhosseini optimized the steam reforming of methane in a fixed bed reactor considering a multi objective optimization problem [26]. The single optimal solution was selected from developed Pareto frontier by various decision-making methods such Shannon Entropy, LINMAP and TOPSIS. The main objective of this study is to optimize the operating condition of methanol oxidation process over iron–molybdenum oxide catalyst to achieve maximum formaldehyde production and selectivity considering a multi-objective optimization model. The Pareto front is developed and the single optimal point is selected from developed optimal Pareto front by TOPSIS decision-making method. In Section 2, Formox process to produce formaldehyde is explained. In Sections 3–5 the considered reaction kinetic, developed mathematical model and selected procedure to find the optimal process condition are presented, respectively. The results and discussion section consist of the model validation, simulation results, sensitivity analysis and results of optimized reactor subsections. 2. Process description Methanol oxidation over the iron–molybdenum oxide catalyst is one of the main methods to produce formaldehyde. In the considered domestic Iranian plant, the methanol oxidation reaction occurs in a multi-tubular fixed-bed reactor. The tubes of reactor are filled by the catalyst plates and light oil as the cooling liquid flows inside the shell side to remove heat from the reaction and keeps the tube surface at a uniform temperature. The used catalyst in the reactor is in the form of rings, with the diameter and height of about 5 mm. Methanol is mixed with excess air, preheated and fed to the reactor. Feed is converted to the formaldehyde over the catalyst surface and product stream is fed to the distillation section. In the separation section, formaldehyde is separated from reactor effluent. The specification of reactor and feed of considered industrial reactor are tabulated in Table 1. 3. Reaction scheme and kinetics Methanol oxidation reaction is highly exothermic. Through the oxidation reaction, methanol reacts with oxygen and formaldehyde is produced.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 2 Reactions rate constants and the adsorption equilibrium constants. Reaction rate constant k1 (mol g/cat/h kPa−0.5 ) k2 (mol g/cat/h kPa−0.5 ) k3 (mol g/cat/h kPa−0.5 )
45 × 106 40,320 24,953
Reaction equilibrium constant 27 Ka (kPa−0.5 )
CH3 OH +
1 O2 → HCHO + H2 O 2
E1 (J/mole) E2 (J/mole) E3 (J/mole)
79,500 66,900 62,800
Ea (J/mole)
8368
energy balances, pressure drop equation for the solid and fluid phases and used correlation to estimate physical properties are listed below. In the gas phase:
Formaldehyde oxidation to carbon monoxide and methanol dehydration are the main side reactions that occur over the catalyst surface.
1 HCHO + O2 → CO + H2 O 2
H298 = −233200 kJ/kmol
(2)
2 CH3 OH → (CH3 )2 O + H2 O
H298 = 19680 kJ/kmol
(3)
r2 =
r3 =
k1 e(E1 /RT ) pM 0.5 1 + Ka e(Ea /RT ) pM 0.5
k2 e(E2 /RT ) pF 0.5
1 + pF 0.5
k3 e(E3 /RT ) pM 0.5 1 + Ka e(Ea /RT ) pM 0.5
(4)
(6)
4. Mathematical modeling 4.1. Reactor modeling In this research, a one-dimensional heterogeneous model is developed to analyze the performance of methanol oxidation reactor at steady state condition. In the considered mathematical model, the following assumptions are adopted: •
•
•
•
•
−
1 g ∂ (Ft .T g ) π Di C + av h f ( T s − T g ) − U (T g − T c ) = 0 Ac p ∂ z Ac
(8)
Over the solid phase:
av ckgi ygi − ysi + ρb
3
ηi r i = 0
(9)
i=1
a v h f ( T g − T s ) + ρb
3 i=1
ηri (−Hi ) = 0
(10)
1 ∂ Ft + ρb ηi ri, j = 0 Ac ∂ z 6
3
(11)
j=1 i=1
The reaction rate constants and the adsorption equilibrium constants for all reactions are tabulated in Table 2 [19,22].
•
(7)
−
(5)
g 1 ∂ Fi + av ckgi ysi − ygi = 0 Ac ∂ z
Total mass balance could be written as:
The rate of main and side reactions are [19,22]:
−
H298 = −158400 kJ/kmol (1)
r1 =
3
The reactor is operated at steady-state conditions. In the case of flow around spheres at high particle Reynolds number (300 < Rep < 105 ), the flow is fully turbulent. Since Rep is 3230, it is assumed that the flow regime is fully turbulent and feed flows uniformly (Plug) along the reactor. UD Radial Peclet number, Drp , represents the ratio of axial mass transport to the radial diffusion. In the methanol oxidation reactor, radial Peclet catalyst is about 1700. Since Per is larger than 1, radial diffusion of mass and energy is negligible [27].
(−r )ρB D p U D p De , axial dispersion of mass is negligible. U CA (−r )ρ D UD Value of UC B p and Dep are 10−4 and 9100, respectively A Since
[27]. hd Biot number, k p , represents the ratio of conductive heat transport in body to convective heat transfer from surface. In the methanol oxidation reactor, Biot number of catalyst is about 0.014. Since it is smaller than 0.1, temperature distribution in catalyst is negligible and lump body assumption is valid [28]. Heat loss from reactor body to surrounding has been neglected.
To develop mass and energy balance equations, a differential element along axial direction of the reactor is considered and governing equations are written over the element. The mass and
Pressure drop along the bed is calculated by Ergun equation as [29]:
(1 − ε )u2g ρ dP (1 − ε )2 μug = 150 + 1.75 2 3 dz ε3 d p ε dp
(12)
In the mass and energy equations, ηi is effectiveness factor that is defined as the average reaction rate considering internal diffusion divided by the average reaction rate if the rate is evaluated at surface concentration. In this research, the effectiveness factor is calculated based on the dusty gas model [27,30]. In the heterogeneous models, the estimation of heat and mass transfer resistance between phases, estimation of physical properties of chemical species and overall heat transfer coefficient between shell and tube sides is necessary. The correlations used to calculate the physical properties and mass and heat transfer coefficients are summarized in Table 3. 4.2. Numerical solution The developed mass and energy governing equations, kinetic expressions and selected auxiliary correlations to predict physical property create a set of nonlinear ordinary differential equations. The developed set of equations is solved numerically with 4th order Runge–Kutta method. The differential equations were programmed in Matlab 2016 with absolute tolerance of 10−6 . 5. Process optimization 5.1. Multi objective optimization problem Multi-objective is an area of multiple criteria decision making that handles mathematical optimization problems involving more than one objective function. In multi-objective problem, there is not a single global solution to optimize all objectives, simultaneously. In that case, there is a Pareto frontier that indicates a set of compromised trade-off solutions. A solution is called nondominated or Pareto optimal if none of objective functions can be improved in value without degrading one or more of the other objective values. Indeed, all points on the Pareto set are equivalent and proposing many options to the decision makers who can find a single optima solution point [35].
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 3 Physical properties, mass and heat transfer correlations. Parameter
Equation
Reference
Component heat capacity Mixture heat capacity Heat transfer coefficient between gas phase and reactor wall
CPi = a + bT + cT2 + dT3 CP = Ni=1 yi CPi h ( CPKμ )2/3 = 0.ε458 ( ρ uμd p )−0.407 CP ρμ B
[31]
Mass transfer coefficient between gas and solid phases
kgi = 1.17Re−0.42 Sci−0.67 ug × 103
[32]
Re p = S ci = Dim =
Mixture mass diffusion coefficient
2ρ R p ug
μ μ
ρ Dim ×10−4 1−yi yi
Binary mass diffusion coefficient
Di j =
Overall heat transfer coefficient
1 U
Catalyst effectiveness factor
η = ∫ rrMMs dv
1/Mi +1/M j
[34]
2
P (v3ci/2 +v3c /j 2 ) 1 hi
=
[33] √
i= j D ij
10−7 T 3/2
v
+
Ai ln(Do /Di ) 2π LKw
+
Ai 1 Ao ho
[27,30]
0
5.2. Decision making method In psychology, decision-making is regarded as the cognitive process resulting in the selection of a belief or a course of action among several alternative possibilities. In the other word, decisionmaking is a process to identify and choosing alternatives based on preferences of the decision-maker. TOPSIS is one of the multicriteria decision analysis methods. In this method, the alternative with the shortest geometric distance from the positive ideal solution and the longest geometric distance from the negative ideal solution is selected as optimal solution. TOPSIS is a method of compensatory aggregation that compares a set of alternatives by identifying weights for each criterion, normalizing scores for each criterion and calculating the geometric distance between each alternative, non-ideal and ideal points.
Table 4 Comparison between simulation results and plant data for industrial reactor. Item
Industrial reactor
Model
Absolute error %
Formaldehyde (kg/h) Carbon monoxide (kg/h) Dimethyl ether (kg/h) Water (kg/h) Conversion of methanol Selectivity of formaldehyde Yield of formaldehyde
2857.3 360.4 133.4 2334.9 0.981 85.75 92.41
2885.7 357.3 131.8 2327.6 0.988 86.02 93.33
0.99 0.86 1.19 0.31 0.71 0.31 0.99
600
580
5.3. Objectives and constraints
6. Results and discussion
Temperature, K
In the chemical reactors, production capacity of desired product and process selectivity are two main key parameters that have a significant effect on the process cost and benefit. Generally, the chemical processes with higher reactant conversion and process selectivity are more attractive. In this research, considering formaldehyde production capacity and selectivity as objectives, the Pareto optimal front is developed by Non-sorting Genetic Algorithm II. The feed temperature, coolant temperature and air to methanol ratio have been selected as decision variables based on the sensitivity analysis. Then, a single optimum solution is selected from developed Pareto front by TOPSIS as an efficient decisionmaking method.
560
540
520
500
480
460 0
0.2
0.4 Length of reactor, m
0.6
6.1. Model validation Fig. 1. Predicted temperature profile along the conventional system.
In this section, developed model for methanol oxidation process is validated against formaldehyde synthesis reactor under the plant operating condition that is known as conventional condition. Table 4 shows the comparison between simulation results and plant data. The plant data was taken from a Domestic Chemical Company in Iran. It is observed that the plant data have a good agreement with the simulation data. 6.2. Conventional reactor In this section, the predicted component molar flow rate, temperature, conversion and selectivity are presented at the conventional condition. Fig. 1 shows the predicted temperature profile
along the reactor. Since the net of reactions is exothermic, temperature increases and a hot spot is developed at the first half of reactor. Then, higher heat removal from reaction zone by the cooling medium compared to the generated heat through reactions, temperature decreases and approaches toward the coolant temperature at the last half of reactor. Fig. 2(a-b) shows the molar flow rate of methanol, formaldehyde, oxygen, water, carbon monoxide and dimethyl ether along the reactor. It appears from Fig. 2(a) that methanol and oxygen content decrease along the reactor. Since methanol is the limiting reactant, it is completely consumed in the reactor. Formaldehyde flow rate increases along the reactor and approaches
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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90
140
80
120 70
100
Selectivity of formaldehyde
Flow rate, kmol/h
60
80
60
40 Methanol
40
30
20
Oxygen Water
20
Formaldehyde
0
10
0
0
0.2
(a)
0.4 Length of reactor, m
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
14
Fig. 3. Selectivity of formaldehyde along the reactor length.
12
reactant in the system. It appears that formaldehyde selectivity increases sharply along the reactor and after a maximum point decreases smoothly. At the entrance of reactor, the minimum selectivity appears due to maximum methanol concentration. Since methanol is consumed through the methanol oxidation reaction to produce formaldehyde, selectivity increases and approaches toward the maximum point. After that, the formaldehyde conversion to dimethyl ether decreases selectivity in the process.
10
Flow rate, kmol/h
50
8
6
6.3. Sensitivity analysis
4
2 Carbon monoxide Dimethyl ether
0 0
(b)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
Fig. 2. (a-b) Molar flow rate of methanol, formaldehyde, oxygen, water, carbon monoxide and dimethyl ether along the conventional reactor.
98 kmol/h. It appears from Fig. 2(b) that molar flow rate of dimethyl ether and carbon monoxide increase along the reactor. Formaldehyde oxidation and methanol dehydration reactions decrease process selectivity. Since the source of dimethyl ether is methanol dehydration, and methanol is completely consumed in the first half of reactor, dimethyl ether flow rate remains constant at the last half part of reactor. Formaldehyde oxidation to carbon monoxide increases carbon monoxide concentration along the reactor and it decreases process selectivity at the second half of reactor. Fig. 3 presents the process selectivity profile along reactor at steady state condition. The selectivity of a reaction is defined as the ratio of desired product formed (in moles) to the consumed
In this section, the effect of feed temperature, coolant temperature and air to methanol ratio on the formaldehyde production capacity and selectivity is investigated. Fig. 4(a-b) shows the effect of feed and coolant temperature on the production rate and selectivity. It appears that there is an optimum value for coolant temperature to achieve maximum formaldehyde production and selectivity. Although feed temperature has an insignificant effect on production capacity, it changes process selectivity considerably. At high coolant temperature increasing feed temperature increases process selectivity, while it decreases selectivity at low coolant temperatures. Fig. 5(a-b) shows the effect of feed temperature and air to methanol ratio on the production rate and selectivity. It appears that there is an optimum value for air to methanol ratio to achieve the maximum formaldehyde production. Although feed temperature has an insignificant effect on the production capacity at low air to methanol ratios, it increases production rate at high air to methanol ratios. It appears that feed temperature influences the optimum air to methanol ratio to achieve maximum production rate and selectivity. At high air to methanol ratios increasing feed temperature increases process selectivity, while it decreases selectivity at low air to methanol ratios. Presented results show that there are optimum values for feed temperature, air to methanol ratio and coolant temperature to achieve maximum formaldehyde production rate and selectivity.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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100
90
Flow rate of formaldehyde, kmol/h
80
70
60
50
40
30
20 560 540 520
(a)
500
400
420
440
500
480
460
Feed temperature, K
Coolant temperature, K 88 86 84
Selectivity of formaldehyde
82 80 78 76 74 72 70 68 480
560
460
540
440
520
(b)
500
Coolant temperature, K
400
420
Feed temperature, K
Fig. 4. Effect of feed temperature and coolant temperature on (a) the formaldehyde production capacity, (b) process selectivity.
6.4. Optimized reactor In this section the results of optimized reactor is presented and compared with the conventional process. It is mentioned that the selected decision variables are feed temperature, coolant temperature and air to methanol ratio. In addition, formaldehyde mole
flow rate and process selectivity are selected as the objective functions. Based on the sensitivity analysis results, coolant temperature and air to methanol ratio are more effective compared to the feed temperature and have a considerable effect on the objective functions. Fig. 6 shows the Pareto front of selected objectives. It is appeared that there is a conflict between objectives,
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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99
98
Flow rate of formaldehyde, kmol/h
97
96
95
94
93
92 20 18
(a)
16
14 12 10 8
430
Air to methanol ratio (N)
460
450
440
470
480
490
Feed temperature, K
87.3 87.2 87.1
Selectivity of formaldehyde
87 86.9 86.8 86.7 86.6 86.5 86.4 86.3 490
8 10
480
12
470
14
460
16
450 18
440
(b)
430
Feed temperature, K
20
Air to methanol ratio (N)
Fig. 5. Effect of feed temperature and air to methanol ratio on (a) the formaldehyde production capacity and (b) process selectivity.
so maximum formaldehyde production rate occurs at minimum process selectivity. The maximum formaldehyde production rate and process selectivity are 98.4 kmol/h and 87.275, respectively. In this research, a single optimum solution is selected from developed Pareto front by TOPSIS as an efficient decision-making method.
Table 5 shows the calculated optimal values of decision variables and comparison between results of optimized and conventional reactors. It is appeared that production capacity and selectivity are improved about 3.35% and 1.43% at the obtained optimal condition compared to the conventional condition. Fig. 7 shows temperature profile along the optimal and conventional reactors.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 5 Calculated optimal operation conditions of formaldehyde reactor. Optimal condition
Conventional
Improvement %
467 540 8.33
446 543 17.9
– – –
2953.85 87.25
2857.3 86.02
3.35 1.43
Decision variables Inlet temperature (K) Coolant temperature (K) Air to methanol ratio (N) Objective functions Formaldehyde rate (kg/h) Selectivity
87.28
100
87.275
90 87.27
80 87.265
Formaldehyde mole flow rate, kmol/h
Process selectivity
70 87.26 87.255 87.25 87.245 87.24 87.235 87.23
60 50 40 30 20 Optimal conditions
10 97.9
98
98.1
98.2
98.3
98.4
Conventional conditions
Formaldehyde mole flow rate, kmol/h
0
Fig. 6. Developed Pareto front based on the multi-objective genetic algorithm.
0
0.1
0.2
(a)
0.3
0.4
0.5
0.6
0.7
Length of reactor, m 90
600
80
580
70
560
Selectivity of formaldehyde
60
Temperature, K
540
520
500
50 40 30 20
480 Optimal conditions Conventional conditions
10 460
Optimal conditions Conventional conditions
0 0
440 0
0.2
0.4
0.6
Length of reactor, m Fig. 7. Temperature profile in the optimal and conventional reactor.
(b)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
Fig. 8. (a) Mole flow rate of formaldehyde and (b) process selectivity along the optimized and conventional reactors.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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Due to higher rate of heat removal from reaction zone compared to the heat generation, temperature decreases after a maximum point and approaches toward the coolant temperature. The results show that there is a uniform temperature profile along the optimized reactor, while hot spot formation is one of the main problem in the conventional system. It appears that the maximum temperatures along the conventional and optimized reactors are 600 °C and 568 °C, respectively. The predicted temperature profile proves the performance and feasibility of optimized reactor compared to the conventional system. Fig. 8(a-b) depicts mole flow rate of formaldehyde and process selectivity along the optimized and conventional reactors. It appears from Fig. 8 that formaldehyde flow rate increases uniformly along the optimized reactor and approaches to 98.36 kmol/h. The higher conversion appears at the first part of conventional reactor compared to the optimized process due to the higher temperature. The priority of optimized reactor over the conventional reactor is determined at the last half part of reactor that formaldehyde concentration approaches toward the equilibrium in the conventional reactor. It appears that operating at the optimized condition increases selectivity from 86.02% to 87.25%. 7. Conclusion In this research, the methanol oxidation process over iron– molybdenum oxide catalyst was modeled based on the mass and energy conservation laws. Comparison between simulation results and plant data proved the accuracy of the developed model and considered assumptions. Then, based on the sensitivity analysis results, feed temperature, coolant temperature and airto-methanol molar ratio were selected as decision variable to maximize formaldehyde production and selectivity considering a multi-objective optimization model. Based on the developed mathematical model of the process and formulated multi-objective optimization model, Pareto optimal front was obtained by nonsorting multi-objective genetic algorithm and a single optimal point was selected from developed optimal Pareto front by TOPSIS decision-making method. It appears that the production capacity and selectivity are improved about 3.35% and 1.43% at the optimal condition compared to conventional process. Also, the simulation results showed that there is a uniform temperature profile along the optimized reactor, while hot spot formation is one of the main problems in the conventional process. References [1] Gerberich HR, Seaman GC. Formaldehyde. Kirk-Othmer encyclopedia of chemical technology. John Wiley & Sons, Inc.; 20 0 0. [2] Reuss G, Disteldorf W, Gamer AO, Hilt A. Formaldehyde. Ullmann’s encyclopedia of industrial chemistry. John Wiley & Sons, Inc.; 20 0 0. [3] Chauvel A, Courty P, Maux R, Petitpas C. Select best formaldehyde catalyst. Hydrocarbon Process 1973;52(9):179–84. [4] Soares APV, Portela MF, Kiennemann A. Methanol selective oxidation to formaldehyde over iron-molybdate catalysts. Catal Rev 2005;47(1):125–74. [5] Gu Z, Hohn KL. Catalytic oxidation of methanol on nanoscale copper oxide and nickel oxide. Ind Eng Chem Res 2004;43(1):30–5. [6] Isaguliants G, Belomestnykh I. Selective oxidation of methanol to formaldehyde over V–Mg–O catalysts. Catal Today 20 05;10 0(3):441–5.
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[7] Niwa M, Igarashi J. Role of the solid acidity on the MoO3 loaded on SnO2 in the methanol oxidation into formaldehyde. Catal Today 1999;52(1):71–81. [8] Otsuka K, Hatano M. The catalysts for the synthesis of formaldehyde by partial oxidation of methane. J Catal 1987;108(1):252–5. [9] Ramachandra B, Choi JS, Choo K-Y, Sung J-S, Song S-D, Kim T-H. Partial oxidation of methanol to formaldehyde on Molybdenum based mixed oxide catalyst. Catal Lett 2005;105(1-2):23–7. [10] Wang Q, Madix RJ. Partial oxidation of methanol to formaldehyde on a model supported monolayer vanadia catalyst: vanadia on TiO2 . Surf Sci 2002;496(1):51–63. [11] Wong G, Kragten D, Vohs J. The oxidation of methanol to formaldehyde on TiO2 supported vanadia films. J Phys Chem B 2001;105(7):1366–73. [12] Dai WL, Cao Y, Ren LP, Yang XL, Xu JH, Li HX, et al. Ag–SiO2 –Al2 O3 composite as highly active catalyst for the formation of formaldehyde from the partial oxidation of methanol. J Catal 2004;228(1):80–91. [13] Wachs IE, Madix RJ. The oxidation of ethanol on Cu and Ag catalysts. Appl Surf Sci 1978;1(3):303–28. [14] Döbler J, Pritzsche M, Sauer J. Oxidation of methanol to formaldehyde on supported vanadium oxide catalysts compared to gas phase molecules. J Am Chem Soc 2005;127(31):10861–8. [15] Andersson A, Holmberg J, Häggblad R. Process improvements in methanol oxidation to formaldehyde: application and catalyst development. Topics Catal 2016;59(17-18):1589–99. [16] Adkins H, Peterson WR. The oxidation of methanol with air over iron, molybdenum, and iron-molybdenum oxides. Journal of the American Chemical Society 1931;53(4):1512–20. [17] Galvanin F, Cao E, Al-Rifai N, Dua V, Gavriilidis A. Optimal design of experiments for the identification of kinetic models of methanol oxidation over silver catalyst. Chim Oggi-Chem Today 2015;33(3):51–6. [18] Chapman S, Brookes C, Bowker M, Gibson EK, Wells PP. Design and stabilisation of a high area iron molybdate surface for the selective oxidation of methanol to formaldehyde. Faraday Discuss 2016;188:115–29. [19] Windes LC, Schwedock MJ, Harmon Ray W. Steady state and dynamic modelling of a packed bed reactor for the partial oxidation of methanol to formaldehyde I. Model development. Chem Eng Commun 1989;78(1):1–43. [20] Faliks A, Yetter R, Floudas C, Bernasek S, Fransson M, Rabitz H. Optimal control of catalytic methanol conversion to formaldehyde. J Phys Chem A 2001;105(10):2099–105. [21] Yang C, Xu N, Shi J. Experimental and modeling study on a packed-bed membrane reactor for partial oxidation of methane to formaldehyde. Ind Eng Chem Res 1998;37(7):2601–10. [22] Moustafa T. Simulation of the industrial packed bed catalytic reactor for the partial oxidation of methanol to formaldehyde. Dev Chem Eng Min Process 2003;11(3-4):337–47. [23] Rangaiah GP, Bonilla-Petriciolet A. Multi-objective optimization in chemical engineering: developments and applications. John Wiley & Sons; 2013. [24] Elnashaie SS, Abashar ME, Al-Ubaid AS. Simulation and optimization of an industrial ammonia reactor. Ind Eng Chem Res 1988;27(11):2015–22. [25] Kordabadi H, Jahanmiri A. Optimization of methanol synthesis reactor using genetic algorithms. Chem Eng J 2005;108(3):249–55. [26] Farsi M, Shahhosseini H. A modified membrane SMR reactor to produce large-scale syngas: modeling and multi objective optimization. Chem Eng Process: Process Intensif 2015;97:169–79. [27] Fogler HS. Elements of chemical reaction engineering. 4th ed. Prentice Hall; 2005. [28] Holman J. Heat transfer. 9th ed. McGraw-Hill; 2002. [29] Ergun S. Fluid flow through packed columns. Chem Eng Prog. 1952;48:89–94. [30] Gonzo E, Gottifredi J. Steady state simulation of a packed bed reactor for the partial oxidation of methanol to formaldehyde. Influence of diffusional phenomena and catalyst activity distribution within the pellets. Chem Eng Commun 1998;168(1):127–43. [31] Cussler EL. Diffusion: mass transfer in fluid systems. Cambridge University Press; 2009. [32] Smith JM. Chemical engineering kinetics. McGraw-Hill; 1981. [33] Wilke C. Estimation of liquid diffusion coefficients. Chem Eng Prog 1949;45(3):218–24. [34] Reid RC, Prausnitz JM, Poling BE. The properties of gases and liquids. 5th ed. McGraw-Hill; 2004. [35] Madetoja E, Ruotsalainen H, Mönkkönen V-M, Hämäläinen J, Deb K, editors. Visualizing multi-dimensional Pareto-optimal fronts with a 3D virtual reality system. Computer science and information technology; 2008.
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Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor H. Ghahraloud, M. Farsi∗ Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran
a r t i c l e
i n f o
Article history: Received 31 August 2016 Revised 2 October 2017 Accepted 4 October 2017 Available online xxx Keywords: Methanol oxidation Process modeling Multi-objective optimization Pareto front TOPSIS decision making
a b s t r a c t The main objective of this study is modeling and optimization of methanol oxidation over ironmolybdenum oxide catalyst in a fixed bed reactor. The considered process is modeled based on the mass and energy balance equations at steady state condition. To verify accuracy of the proposed model and considered assumptions, the simulation results are compared with the plant data. Then, the effect of feed temperature, coolant temperature and air-to-methanol molar ratio on the reactor performance is investigated. In addition, considering formaldehyde production capacity and selectivity as objectives, a multi-objective optimization problem is formulated considering feed and coolant temperature, and air to methanol ratio as decision variables. Based on the developed mathematical model of the process and multi-objective optimization model, Pareto optimal front is obtained by non-sorting multi-objective genetic algorithm. Then, the single optimal point is selected from developed optimal Pareto front by TOPSIS decision-making method. The performance of the optimized reactor is compared with the conventional reactor at steady state condition. © 2017 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
1. Introduction Formaldehyde as the simplest aldehyde is an important compound to produce complex chemicals and polymers such as urea formaldehyde resin, melamine resin, phenol formaldehyde resin and polyoxymethylene plastics [1]. Formaldehyde is produced industrially from methanol through different processes, including partial oxidation and dehydrogenation in the presence of silver crystal or silver gauze with excess methanol, and oxidation only with air in the presence of a modified iron–molybdenum– vanadium oxide catalyst and excess air [2]. The main differences between the production methods are catalyst type, operating condition and the feed concentration. The methanol oxidation over silver-based catalyst at 60 0–70 0 °C is the oldest process to produce formaldehyde commercialized by BASF and ICI [1,3,4]. In this process, reaction temperature and conversion depend on the methanol concentration in feed stream. In Formox process, commercialized by Johnson Matthey Process Technologies, methanol and oxygen react at 30 0–40 0 °C in presence of iron–molybdenum oxide catalyst [1]. Generally, the iron– molybdenum oxide catalyst has attracted more attention compared to the silver catalyst due to lower investment and operating costs.
∗
Corresponding author. E-mail address: [email protected] (M. Farsi).
However, sensitivity against operating condition is the main disadvantage of iron–molybdenum oxide catalyst [3]. Many researchers have focused on the catalyst synthesis and mechanism of methanol oxidation to formaldehyde [5–14]. Andersson et al. presented a good overview describing the historical and present developments on the methanol oxidation to formaldehyde from 1950s [15]. Generally, vanadium pentoxide catalyst is the first metal oxide used in the methanol oxidation process [1]. Adkins and Peterson introduced iron–molybdenum oxide as methanol oxidation catalyst due to high selectivity and thermal resistance [16]. Galvanin et al. proposed a model-based design of experiments procedure to estimate the kinetic parameters of methanol oxidation on silver catalyst [17]. Chapman et al. showed that the performance of Mo-enriched, bulk ferric molybdate, employed commercially for selective oxidation of methanol to formaldehyde, is limited by a low surface area [18]. The results proved that core–shell, multi-component oxides offer new routes for improving catalytic performance and activity. Windes et al. modeled partial oxidation of methanol considering heterogeneous and pseudo homogeneous models at steady state condition. The results showed that the considered models are capable to predict hot spot position and yield. In addition, it was shown that coolant temperature has a significant effect on the reactor performance compared to the feed temperature [19]. Faliks et al. modeled formaldehyde production over iron–molybdenum oxide catalyst at steady state condition. The results showed that the distribution of heat flux effects
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Nomenclature av Ac Cp C D dp Ei Dij Dim F hf hi ho
H i ki Ka L P Pi ri R Tg Tc Ts ug U g yi ysi z
specific surface area of catalyst pellet (m2 /m3 ) cross section area of each tube (m2 ) specific heat of the gas at constant pressure (J/mol/K) total concentration (kmol/m3 ) tube diameter (m) catalyst particle diameter (m) activation energy for ith reaction (J/mol) binary diffusion coefficient of component i in j (m2 /s) diffusion coefficient of component i in the mixture (m2 /s) total molar flow rate (mol/s) gas–solid heat transfer coefficient in reactor (W/m2 /K) tube side heat transfer coefficient in reactor (W/m2 /K) shell side heat transfer coefficient in reactor (W/m2 /K) heat of reaction for reaction i (kJ/kmol) reaction rate constant (mol g/cat/h/kPa0.5 ) adsorption equilibrium constant in the rate equation (kPa−0.5 ) reactor length (m) total pressure (kPa) partial pressure of component i (kPa) rate of reaction (mol g/cat/h) Universal gas constant (J/mol/K) bulk gas phase temperature (K) cooling liquid temperature in shell side (K) solid phase temperature (K) velocity of fluid phase (m/s) overall heat transfer coefficient (W/m2 /K) mole fraction of component i in the fluid phase mole fraction of component i on the catalyst surface axial reactor coordinate (m)
Greek letters μ viscosity of gas phase (Pa s) η catalyst effectiveness factor ρ gas density (kg/m3 ) ρ catalytic bed density (kg/m3 ) b ε porosity factor
on the formaldehyde yield [20]. Yang et al. modeled a packed-bed membrane reactor for partial oxidation of methanol to formaldehyde. The simulation results showed that the membrane reactor presents a higher selectivity compared to the conventional process [21]. Moustafa simulated a formaldehyde reactor considering diffusion-reaction kinetic model [22]. The effectiveness factor of reactions was selected as fitting parameters and calculated based on the plant data. Process optimization is the discipline to adjust process condition to operate at desired performance without violating operational, safety and other constraints. Operating the chemical processes at optimal point could decrease cost, energy and risk in the system. There are many researches in the literature that have focused on the optimization of chemical process particularly chemical reactors [23]. Elnashaie et al. developed a heterogeneous model to simulate and optimize an industrial ammonia reactor [24]. The results showed that applying the optimal condition on the system increases ammonia production capacity about 6–7%. Kordabadi and
Table 1 Reactor characteristics and catalyst specification of the conventional process. Parameter
Value
Feed condition Coolant temperature (K) Methanol feed flow rate (kmol/h) Air to methanol ratio Inlet pressure (bar) Inlet temperature (K)
540 102.96 8.325 2.16 467
Reactor characteristics Catalyst bed length (m) Tube internal diameter (m) Number of tubes Bed void fraction
0.77 0.025 7700 0.45
Catalyst particle characteristics Catalyst shape Density (kg/m3 ) Diameter (m) Height to diameter ratio
Ring 10 0 0 0.0048 1
Jahanmiri optimized methanol production in an industrial fixed bed reactor by genetic algorithm [25]. This optimization approach enhanced 2.9% additional yield throughout 4 years. Farsi and Shahhosseini optimized the steam reforming of methane in a fixed bed reactor considering a multi objective optimization problem [26]. The single optimal solution was selected from developed Pareto frontier by various decision-making methods such Shannon Entropy, LINMAP and TOPSIS. The main objective of this study is to optimize the operating condition of methanol oxidation process over iron–molybdenum oxide catalyst to achieve maximum formaldehyde production and selectivity considering a multi-objective optimization model. The Pareto front is developed and the single optimal point is selected from developed optimal Pareto front by TOPSIS decision-making method. In Section 2, Formox process to produce formaldehyde is explained. In Sections 3–5 the considered reaction kinetic, developed mathematical model and selected procedure to find the optimal process condition are presented, respectively. The results and discussion section consist of the model validation, simulation results, sensitivity analysis and results of optimized reactor subsections. 2. Process description Methanol oxidation over the iron–molybdenum oxide catalyst is one of the main methods to produce formaldehyde. In the considered domestic Iranian plant, the methanol oxidation reaction occurs in a multi-tubular fixed-bed reactor. The tubes of reactor are filled by the catalyst plates and light oil as the cooling liquid flows inside the shell side to remove heat from the reaction and keeps the tube surface at a uniform temperature. The used catalyst in the reactor is in the form of rings, with the diameter and height of about 5 mm. Methanol is mixed with excess air, preheated and fed to the reactor. Feed is converted to the formaldehyde over the catalyst surface and product stream is fed to the distillation section. In the separation section, formaldehyde is separated from reactor effluent. The specification of reactor and feed of considered industrial reactor are tabulated in Table 1. 3. Reaction scheme and kinetics Methanol oxidation reaction is highly exothermic. Through the oxidation reaction, methanol reacts with oxygen and formaldehyde is produced.
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 2 Reactions rate constants and the adsorption equilibrium constants. Reaction rate constant k1 (mol g/cat/h kPa−0.5 ) k2 (mol g/cat/h kPa−0.5 ) k3 (mol g/cat/h kPa−0.5 )
45 × 106 40,320 24,953
Reaction equilibrium constant 27 Ka (kPa−0.5 )
CH3 OH +
1 O2 → HCHO + H2 O 2
E1 (J/mole) E2 (J/mole) E3 (J/mole)
79,500 66,900 62,800
Ea (J/mole)
8368
energy balances, pressure drop equation for the solid and fluid phases and used correlation to estimate physical properties are listed below. In the gas phase:
Formaldehyde oxidation to carbon monoxide and methanol dehydration are the main side reactions that occur over the catalyst surface.
1 HCHO + O2 → CO + H2 O 2
H298 = −233200 kJ/kmol
(2)
2 CH3 OH → (CH3 )2 O + H2 O
H298 = 19680 kJ/kmol
(3)
r2 =
r3 =
k1 e(E1 /RT ) pM 0.5 1 + Ka e(Ea /RT ) pM 0.5
k2 e(E2 /RT ) pF 0.5
1 + pF 0.5
k3 e(E3 /RT ) pM 0.5 1 + Ka e(Ea /RT ) pM 0.5
(4)
(6)
4. Mathematical modeling 4.1. Reactor modeling In this research, a one-dimensional heterogeneous model is developed to analyze the performance of methanol oxidation reactor at steady state condition. In the considered mathematical model, the following assumptions are adopted: •
•
•
•
•
−
1 g ∂ (Ft .T g ) π Di C + av h f ( T s − T g ) − U (T g − T c ) = 0 Ac p ∂ z Ac
(8)
Over the solid phase:
av ckgi ygi − ysi + ρb
3
ηi r i = 0
(9)
i=1
a v h f ( T g − T s ) + ρb
3 i=1
ηri (−Hi ) = 0
(10)
1 ∂ Ft + ρb ηi ri, j = 0 Ac ∂ z 6
3
(11)
j=1 i=1
The reaction rate constants and the adsorption equilibrium constants for all reactions are tabulated in Table 2 [19,22].
•
(7)
−
(5)
g 1 ∂ Fi + av ckgi ysi − ygi = 0 Ac ∂ z
Total mass balance could be written as:
The rate of main and side reactions are [19,22]:
−
H298 = −158400 kJ/kmol (1)
r1 =
3
The reactor is operated at steady-state conditions. In the case of flow around spheres at high particle Reynolds number (300 < Rep < 105 ), the flow is fully turbulent. Since Rep is 3230, it is assumed that the flow regime is fully turbulent and feed flows uniformly (Plug) along the reactor. UD Radial Peclet number, Drp , represents the ratio of axial mass transport to the radial diffusion. In the methanol oxidation reactor, radial Peclet catalyst is about 1700. Since Per is larger than 1, radial diffusion of mass and energy is negligible [27].
(−r )ρB D p U D p De , axial dispersion of mass is negligible. U CA (−r )ρ D UD Value of UC B p and Dep are 10−4 and 9100, respectively A Since
[27]. hd Biot number, k p , represents the ratio of conductive heat transport in body to convective heat transfer from surface. In the methanol oxidation reactor, Biot number of catalyst is about 0.014. Since it is smaller than 0.1, temperature distribution in catalyst is negligible and lump body assumption is valid [28]. Heat loss from reactor body to surrounding has been neglected.
To develop mass and energy balance equations, a differential element along axial direction of the reactor is considered and governing equations are written over the element. The mass and
Pressure drop along the bed is calculated by Ergun equation as [29]:
(1 − ε )u2g ρ dP (1 − ε )2 μug = 150 + 1.75 2 3 dz ε3 d p ε dp
(12)
In the mass and energy equations, ηi is effectiveness factor that is defined as the average reaction rate considering internal diffusion divided by the average reaction rate if the rate is evaluated at surface concentration. In this research, the effectiveness factor is calculated based on the dusty gas model [27,30]. In the heterogeneous models, the estimation of heat and mass transfer resistance between phases, estimation of physical properties of chemical species and overall heat transfer coefficient between shell and tube sides is necessary. The correlations used to calculate the physical properties and mass and heat transfer coefficients are summarized in Table 3. 4.2. Numerical solution The developed mass and energy governing equations, kinetic expressions and selected auxiliary correlations to predict physical property create a set of nonlinear ordinary differential equations. The developed set of equations is solved numerically with 4th order Runge–Kutta method. The differential equations were programmed in Matlab 2016 with absolute tolerance of 10−6 . 5. Process optimization 5.1. Multi objective optimization problem Multi-objective is an area of multiple criteria decision making that handles mathematical optimization problems involving more than one objective function. In multi-objective problem, there is not a single global solution to optimize all objectives, simultaneously. In that case, there is a Pareto frontier that indicates a set of compromised trade-off solutions. A solution is called nondominated or Pareto optimal if none of objective functions can be improved in value without degrading one or more of the other objective values. Indeed, all points on the Pareto set are equivalent and proposing many options to the decision makers who can find a single optima solution point [35].
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 3 Physical properties, mass and heat transfer correlations. Parameter
Equation
Reference
Component heat capacity Mixture heat capacity Heat transfer coefficient between gas phase and reactor wall
CPi = a + bT + cT2 + dT3 CP = Ni=1 yi CPi h ( CPKμ )2/3 = 0.ε458 ( ρ uμd p )−0.407 CP ρμ B
[31]
Mass transfer coefficient between gas and solid phases
kgi = 1.17Re−0.42 Sci−0.67 ug × 103
[32]
Re p = S ci = Dim =
Mixture mass diffusion coefficient
2ρ R p ug
μ μ
ρ Dim ×10−4 1−yi yi
Binary mass diffusion coefficient
Di j =
Overall heat transfer coefficient
1 U
Catalyst effectiveness factor
η = ∫ rrMMs dv
1/Mi +1/M j
[34]
2
P (v3ci/2 +v3c /j 2 ) 1 hi
=
[33] √
i= j D ij
10−7 T 3/2
v
+
Ai ln(Do /Di ) 2π LKw
+
Ai 1 Ao ho
[27,30]
0
5.2. Decision making method In psychology, decision-making is regarded as the cognitive process resulting in the selection of a belief or a course of action among several alternative possibilities. In the other word, decisionmaking is a process to identify and choosing alternatives based on preferences of the decision-maker. TOPSIS is one of the multicriteria decision analysis methods. In this method, the alternative with the shortest geometric distance from the positive ideal solution and the longest geometric distance from the negative ideal solution is selected as optimal solution. TOPSIS is a method of compensatory aggregation that compares a set of alternatives by identifying weights for each criterion, normalizing scores for each criterion and calculating the geometric distance between each alternative, non-ideal and ideal points.
Table 4 Comparison between simulation results and plant data for industrial reactor. Item
Industrial reactor
Model
Absolute error %
Formaldehyde (kg/h) Carbon monoxide (kg/h) Dimethyl ether (kg/h) Water (kg/h) Conversion of methanol Selectivity of formaldehyde Yield of formaldehyde
2857.3 360.4 133.4 2334.9 0.981 85.75 92.41
2885.7 357.3 131.8 2327.6 0.988 86.02 93.33
0.99 0.86 1.19 0.31 0.71 0.31 0.99
600
580
5.3. Objectives and constraints
6. Results and discussion
Temperature, K
In the chemical reactors, production capacity of desired product and process selectivity are two main key parameters that have a significant effect on the process cost and benefit. Generally, the chemical processes with higher reactant conversion and process selectivity are more attractive. In this research, considering formaldehyde production capacity and selectivity as objectives, the Pareto optimal front is developed by Non-sorting Genetic Algorithm II. The feed temperature, coolant temperature and air to methanol ratio have been selected as decision variables based on the sensitivity analysis. Then, a single optimum solution is selected from developed Pareto front by TOPSIS as an efficient decisionmaking method.
560
540
520
500
480
460 0
0.2
0.4 Length of reactor, m
0.6
6.1. Model validation Fig. 1. Predicted temperature profile along the conventional system.
In this section, developed model for methanol oxidation process is validated against formaldehyde synthesis reactor under the plant operating condition that is known as conventional condition. Table 4 shows the comparison between simulation results and plant data. The plant data was taken from a Domestic Chemical Company in Iran. It is observed that the plant data have a good agreement with the simulation data. 6.2. Conventional reactor In this section, the predicted component molar flow rate, temperature, conversion and selectivity are presented at the conventional condition. Fig. 1 shows the predicted temperature profile
along the reactor. Since the net of reactions is exothermic, temperature increases and a hot spot is developed at the first half of reactor. Then, higher heat removal from reaction zone by the cooling medium compared to the generated heat through reactions, temperature decreases and approaches toward the coolant temperature at the last half of reactor. Fig. 2(a-b) shows the molar flow rate of methanol, formaldehyde, oxygen, water, carbon monoxide and dimethyl ether along the reactor. It appears from Fig. 2(a) that methanol and oxygen content decrease along the reactor. Since methanol is the limiting reactant, it is completely consumed in the reactor. Formaldehyde flow rate increases along the reactor and approaches
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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5
90
140
80
120 70
100
Selectivity of formaldehyde
Flow rate, kmol/h
60
80
60
40 Methanol
40
30
20
Oxygen Water
20
Formaldehyde
0
10
0
0
0.2
(a)
0.4 Length of reactor, m
0.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
14
Fig. 3. Selectivity of formaldehyde along the reactor length.
12
reactant in the system. It appears that formaldehyde selectivity increases sharply along the reactor and after a maximum point decreases smoothly. At the entrance of reactor, the minimum selectivity appears due to maximum methanol concentration. Since methanol is consumed through the methanol oxidation reaction to produce formaldehyde, selectivity increases and approaches toward the maximum point. After that, the formaldehyde conversion to dimethyl ether decreases selectivity in the process.
10
Flow rate, kmol/h
50
8
6
6.3. Sensitivity analysis
4
2 Carbon monoxide Dimethyl ether
0 0
(b)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
Fig. 2. (a-b) Molar flow rate of methanol, formaldehyde, oxygen, water, carbon monoxide and dimethyl ether along the conventional reactor.
98 kmol/h. It appears from Fig. 2(b) that molar flow rate of dimethyl ether and carbon monoxide increase along the reactor. Formaldehyde oxidation and methanol dehydration reactions decrease process selectivity. Since the source of dimethyl ether is methanol dehydration, and methanol is completely consumed in the first half of reactor, dimethyl ether flow rate remains constant at the last half part of reactor. Formaldehyde oxidation to carbon monoxide increases carbon monoxide concentration along the reactor and it decreases process selectivity at the second half of reactor. Fig. 3 presents the process selectivity profile along reactor at steady state condition. The selectivity of a reaction is defined as the ratio of desired product formed (in moles) to the consumed
In this section, the effect of feed temperature, coolant temperature and air to methanol ratio on the formaldehyde production capacity and selectivity is investigated. Fig. 4(a-b) shows the effect of feed and coolant temperature on the production rate and selectivity. It appears that there is an optimum value for coolant temperature to achieve maximum formaldehyde production and selectivity. Although feed temperature has an insignificant effect on production capacity, it changes process selectivity considerably. At high coolant temperature increasing feed temperature increases process selectivity, while it decreases selectivity at low coolant temperatures. Fig. 5(a-b) shows the effect of feed temperature and air to methanol ratio on the production rate and selectivity. It appears that there is an optimum value for air to methanol ratio to achieve the maximum formaldehyde production. Although feed temperature has an insignificant effect on the production capacity at low air to methanol ratios, it increases production rate at high air to methanol ratios. It appears that feed temperature influences the optimum air to methanol ratio to achieve maximum production rate and selectivity. At high air to methanol ratios increasing feed temperature increases process selectivity, while it decreases selectivity at low air to methanol ratios. Presented results show that there are optimum values for feed temperature, air to methanol ratio and coolant temperature to achieve maximum formaldehyde production rate and selectivity.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9
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Flow rate of formaldehyde, kmol/h
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50
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20 560 540 520
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Feed temperature, K
Coolant temperature, K 88 86 84
Selectivity of formaldehyde
82 80 78 76 74 72 70 68 480
560
460
540
440
520
(b)
500
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400
420
Feed temperature, K
Fig. 4. Effect of feed temperature and coolant temperature on (a) the formaldehyde production capacity, (b) process selectivity.
6.4. Optimized reactor In this section the results of optimized reactor is presented and compared with the conventional process. It is mentioned that the selected decision variables are feed temperature, coolant temperature and air to methanol ratio. In addition, formaldehyde mole
flow rate and process selectivity are selected as the objective functions. Based on the sensitivity analysis results, coolant temperature and air to methanol ratio are more effective compared to the feed temperature and have a considerable effect on the objective functions. Fig. 6 shows the Pareto front of selected objectives. It is appeared that there is a conflict between objectives,
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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Flow rate of formaldehyde, kmol/h
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87.3 87.2 87.1
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87 86.9 86.8 86.7 86.6 86.5 86.4 86.3 490
8 10
480
12
470
14
460
16
450 18
440
(b)
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Feed temperature, K
20
Air to methanol ratio (N)
Fig. 5. Effect of feed temperature and air to methanol ratio on (a) the formaldehyde production capacity and (b) process selectivity.
so maximum formaldehyde production rate occurs at minimum process selectivity. The maximum formaldehyde production rate and process selectivity are 98.4 kmol/h and 87.275, respectively. In this research, a single optimum solution is selected from developed Pareto front by TOPSIS as an efficient decision-making method.
Table 5 shows the calculated optimal values of decision variables and comparison between results of optimized and conventional reactors. It is appeared that production capacity and selectivity are improved about 3.35% and 1.43% at the obtained optimal condition compared to the conventional condition. Fig. 7 shows temperature profile along the optimal and conventional reactors.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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H. Ghahraloud, M. Farsi / Journal of the Taiwan Institute of Chemical Engineers 000 (2017) 1–9 Table 5 Calculated optimal operation conditions of formaldehyde reactor. Optimal condition
Conventional
Improvement %
467 540 8.33
446 543 17.9
– – –
2953.85 87.25
2857.3 86.02
3.35 1.43
Decision variables Inlet temperature (K) Coolant temperature (K) Air to methanol ratio (N) Objective functions Formaldehyde rate (kg/h) Selectivity
87.28
100
87.275
90 87.27
80 87.265
Formaldehyde mole flow rate, kmol/h
Process selectivity
70 87.26 87.255 87.25 87.245 87.24 87.235 87.23
60 50 40 30 20 Optimal conditions
10 97.9
98
98.1
98.2
98.3
98.4
Conventional conditions
Formaldehyde mole flow rate, kmol/h
0
Fig. 6. Developed Pareto front based on the multi-objective genetic algorithm.
0
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0.2
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600
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480 Optimal conditions Conventional conditions
10 460
Optimal conditions Conventional conditions
0 0
440 0
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Length of reactor, m Fig. 7. Temperature profile in the optimal and conventional reactor.
(b)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Length of reactor, m
Fig. 8. (a) Mole flow rate of formaldehyde and (b) process selectivity along the optimized and conventional reactors.
Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003
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Due to higher rate of heat removal from reaction zone compared to the heat generation, temperature decreases after a maximum point and approaches toward the coolant temperature. The results show that there is a uniform temperature profile along the optimized reactor, while hot spot formation is one of the main problem in the conventional system. It appears that the maximum temperatures along the conventional and optimized reactors are 600 °C and 568 °C, respectively. The predicted temperature profile proves the performance and feasibility of optimized reactor compared to the conventional system. Fig. 8(a-b) depicts mole flow rate of formaldehyde and process selectivity along the optimized and conventional reactors. It appears from Fig. 8 that formaldehyde flow rate increases uniformly along the optimized reactor and approaches to 98.36 kmol/h. The higher conversion appears at the first part of conventional reactor compared to the optimized process due to the higher temperature. The priority of optimized reactor over the conventional reactor is determined at the last half part of reactor that formaldehyde concentration approaches toward the equilibrium in the conventional reactor. It appears that operating at the optimized condition increases selectivity from 86.02% to 87.25%. 7. Conclusion In this research, the methanol oxidation process over iron– molybdenum oxide catalyst was modeled based on the mass and energy conservation laws. Comparison between simulation results and plant data proved the accuracy of the developed model and considered assumptions. Then, based on the sensitivity analysis results, feed temperature, coolant temperature and airto-methanol molar ratio were selected as decision variable to maximize formaldehyde production and selectivity considering a multi-objective optimization model. Based on the developed mathematical model of the process and formulated multi-objective optimization model, Pareto optimal front was obtained by nonsorting multi-objective genetic algorithm and a single optimal point was selected from developed optimal Pareto front by TOPSIS decision-making method. It appears that the production capacity and selectivity are improved about 3.35% and 1.43% at the optimal condition compared to conventional process. Also, the simulation results showed that there is a uniform temperature profile along the optimized reactor, while hot spot formation is one of the main problems in the conventional process. References [1] Gerberich HR, Seaman GC. Formaldehyde. Kirk-Othmer encyclopedia of chemical technology. John Wiley & Sons, Inc.; 20 0 0. [2] Reuss G, Disteldorf W, Gamer AO, Hilt A. Formaldehyde. Ullmann’s encyclopedia of industrial chemistry. John Wiley & Sons, Inc.; 20 0 0. [3] Chauvel A, Courty P, Maux R, Petitpas C. Select best formaldehyde catalyst. Hydrocarbon Process 1973;52(9):179–84. [4] Soares APV, Portela MF, Kiennemann A. Methanol selective oxidation to formaldehyde over iron-molybdate catalysts. Catal Rev 2005;47(1):125–74. [5] Gu Z, Hohn KL. Catalytic oxidation of methanol on nanoscale copper oxide and nickel oxide. Ind Eng Chem Res 2004;43(1):30–5. [6] Isaguliants G, Belomestnykh I. Selective oxidation of methanol to formaldehyde over V–Mg–O catalysts. Catal Today 20 05;10 0(3):441–5.
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Please cite this article as: H. Ghahraloud, M. Farsi, Modeling and optimization of methanol oxidation over metal oxide catalyst in an industrial fixed bed reactor, Journal of the Taiwan Institute of Chemical Engineers (2017), https://doi.org/10.1016/j.jtice.2017.10.003